W11.Through a pipe 15.0cm in diameter, water is pumped from the Gefersa River
up to Burayu town, located on the west side of Addis Ababa. Suppose, the
river is at an elevation of 564m, and the village is at an elevation of 2096m.
(a) What is the minimum pressure at which the water must be pumped if it is
to arrive at the town? (b) If 4500m3 are pumped per day, what is the speed
of the water in the pipe?
12.On an unknown temperature scale, the freezing point of water is -15.0°U and
the boiling point is +60.0°U. Develop a linear conversion equation between this
temperature scale and the Fahrenheit scale.
13.A copper telephone wire has essentially no sag between poles 35.0 m apart on a
winter day when the temperature is -20.0°C. How much longer is the wire on
a summer day when TC=35.0°C?
(a) To find the minimum pressure at which the water must be pumped, we can use the following equation:
P = ρgh + (1/2)ρv^2
Where:
P = pressure
ρ = density of water = 1000 kg/m^3
g = acceleration due to gravity = 9.81 m/s^2
h = height difference between the river and the village = 2096m - 564m = 1532m
v = velocity of water in the pipe
Assuming the water is moving with a constant velocity at the exit of the pipe (i.e. v=0 at the river), the equation simplifies to:
P = ρgh
Plugging in the values:
P = (1000 kg/m^3)(9.81 m/s^2)(1532m) = 15,039,720 Pa
Therefore, the minimum pressure at which the water must be pumped is 15,039,720 Pa.
(b) To find the speed of the water in the pipe, we can use the equation of continuity, which states that the volume flow rate is constant in a pipe:
A1v1 = A2v2
Where:
A1 = π(0.15m/2)^2 = 0.01767 m^2 (cross-sectional area of the pipe)
A2 = A1
v1 = velocity of water in the pipe
v2 = velocity of water at the exit of the pipe
Given that 4500m^3 are pumped per day, we can convert this to m^3/s:
4500m^3/(24*3600s) = 0.052 m^3/s
Therefore, the velocity of water in the pipe is:
v1 = 0.052m^3/s / 0.01767m^2 = 2.94 m/s
Therefore, the speed of the water in the pipe is 2.94 m/s.
(c) To find how much longer the wire is on a summer day, we can use the following formula for the change in length due to temperature:
ΔL = Lα(Tf - Ti)
Where:
ΔL = change in length
L = initial length of the wire = 35.0m
α = coefficient of linear expansion for copper = 1.7 x 10^-5 /°C
Tf = final temperature = 35.0°C
Ti = initial temperature = -20.0°C
Plugging in the values:
ΔL = 35.0m * (1.7 x 10^-5 /°C) * (35.0°C - (-20.0°C))
ΔL = 35.0m * 1.7 x 10^-5 /°C * 55.0°C
ΔL = 32 x 10^-3m = 32mm
Therefore, the wire is 32mm longer on a summer day.